Question : The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of the four numbers?
Option 1: 17
Option 2: 14
Option 3: 21
Option 4: 24
Correct Answer: 14
Solution :
Let the 1
st
number be 'x'.
2
nd
number is 'x + 1'.
3
rd
number is 'x + 2'.
And 4
th
number is 'x + 3'.
According to the question,
1
st
number + 2
nd
number = 4
th
number.
⇒ x + x + 1 = x + 3
⇒ x = 2
Putting the value of x we get the numbers 2, 3, 4, and 5.
Their LCM is 60 which satisfies the condition in the question.
The sum of the four numbers = 2 + 3 + 4 + 5 = 14
Hence, the correct answer is 14.
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